The main aim of this paper is to introduce three classes $H^0_{p,q}$, $H^1_{p,q}$ and $TH^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. First, we discuss the starlikeness and convexity of mappings in $H^0_{p,q}$ and $H^1_{p,q}$. Then establish the covering theorem for mappings in $H^1_{p,q}$. Finally, we determine the extreme points of the class $TH^*_{p}$.

The main purpose of this paper is to consider q-sine-based and q-cosine-Based q-Fubini polynomials investigate diverse properties these polynomials. Furthermore, multifarious correlations including q-analogues the Genocchi, Euler Bernoulli polynomials, q-Stirling numbers second kind are derived. Moreover, some approximate zeros q-sinebased in a complex plane examined, lastly, shown using figures.

the main aim of this paper is to introduce three classes $h^0_{p,q}$, $h^1_{p,q}$ and $th^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. first, we discuss the starlikeness and convexity of mappings in $h^0_{p,q}$ and $h^1_{p,q}$. then establish the covering theorem for mappings in $h^1_{p,q}$. finally, we determine the extreme points of the class $th^*_{p}$.